29 8.G.C.9 Math.8.G.9 8.G.C.9 8.GSR.8.4 8.G.9 8.G.9 8.G.9 8.G.C.7 CC.2.3.8.A.1 M08.C-G.3.1.1 8.GSR.8.4 8.GM.1

Volume 8th Grade

Alabama Course of Study Standards: 29
Informally derive the formulas for the volume of cones and spheres by experimentally comparing the volumes of cones and spheres with the same radius and height to a cylinder with the same dimensions. 30 - Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve realworld problems.
Arizona Academic Standards: 8.G.C.9
Understand and use formulas for volumes of cones, cylinders and spheres and use them to solve real-world context and mathematical problems.
Common Core State Standards: Math.8.G.9 or 8.G.C.9 Tennessee Academic Standards: 8.G.C.7
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Georgia Standards of Excellence (GSE): 8.GSR.8.4
Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.
North Carolina - Standard Course of Study: 8.G.9
Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems.
New York State Next Generation Learning Standards: 8.G.9
Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and realworld problems.
Ohio's Learning Standards: 8.G.9
Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres.
Pennsylvania Core Standards: CC.2.3.8.A.1
Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.
Pennsylvania Core Standards: M08.C-G.3.1.1
Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems.
Georgia Standards of Excellence (GSE): 8.GSR.8.4
Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.
Arkansas Academic Standards: 8.GM.1
Apply the formulas for the volume and surface area of cylinders, cones, and spheres to solve real-world and mathematical problems.

Volume of Sphere = \frac{4}{3} π r^{3}

where r is the radius

\begin{array}{rcl} Volume & = & \frac{4}{3} π r^{3} \\ 113.04 {cm}^{3} & = & \frac{4}{3} π r^{3} \\ 113.04 {cm}^{3} & = & \frac{4}{3} (3.14) r^{3} \\ 113.04 {cm}^{3} \div 3.14 & = & \frac{4}{3} (3.14) r^{3} \div 3.14 \\ 36 {cm}^{3} & = & \frac{4}{3} r^{3} \\ 36 {cm}^{3} \times \frac{3}{4} & = & \frac{4}{3} r^{3} \times \frac{3}{4} \\ 27 {cm}^{3} & = & r^{3} \\ 3 cm & = & r \end{array}

Volume of Cylinder = π r^{2} h

where r is the radius and h is the height

\begin{array}{rcl} Volume & = & π r^{2} h \\ 36 π {cm}^{3} & = & π {(3 cm)}^{2} h \\ 36 π {cm}^{3} \div π & = & π {(3 cm)}^{2} h \div π \\ 36 {cm}^{3} & = & (9 {cm}^{2}) h \\ 36 {cm}^{3} \div {9 cm}^{2} & = & (9 {cm}^{2}) h \div {9 cm}^{2} \\ 4 cm & = & h \end{array}

Volume of Cone = \frac{1}{3} π r^{2} h

where r is the radius and h is the height

\begin{array}{rcl} Volume & = & \frac{1}{3} π r^{2} h \\ = & \frac{1}{3} π ({3 cm)}^{2} (2 cm) \\ = & \frac{1}{3} π ({9 cm}^{2}) (2 cm) \\ = & \frac{1}{3} π ({18 cm}^{3}) \\ = & 6 π {cm}^{3} \end{array}

The volume of the cone is 6

π

cubic centimeters.

Volume

Alabama Course of Study Standards: 29

Arizona Academic Standards: 8.G.C.9

Understand and use formulas for volumes of cones, cylinders and spheres and use them to solve real-world context and mathematical problems.

Common Core State Standards: Math.8.G.9 or 8.G.C.9

Tennessee Academic Standards: 8.G.C.7

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Georgia Standards of Excellence (GSE): 8.GSR.8.4

Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.

North Carolina - Standard Course of Study: 8.G.9

Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems.

New York State Next Generation Learning Standards: 8.G.9

Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and realworld problems.

Ohio's Learning Standards: 8.G.9

Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres.

Pennsylvania Core Standards: CC.2.3.8.A.1

Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.

Pennsylvania Core Standards: M08.C-G.3.1.1

Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems.

Georgia Standards of Excellence (GSE): 8.GSR.8.4

Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.

Arkansas Academic Standards: 8.GM.1

Apply the formulas for the volume and surface area of cylinders, cones, and spheres to solve real-world and mathematical problems.

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